Sustainable Energy and Artificial Intelligence

Fuzzy Insulin Dosing Policy Design for Type 1 Diabetes Under Different Pump Constraints: An LMI Approach

Document Type : Original Article

Authors

Mohammadreza Ganji
Mohammadreza Kamali Ardakani
Mahdi Pourgholi

Department of Electrical Engineering, Shahid Beheshti University, Tehran, Iran

https://doi.org/10.61186/seai.2409-1008
Abstract
This paper presents an insulin dosing policy for individuals with Type 1 Diabetes (T1D), utilizing Linear Matrix Inequality (LMI) techniques in combination with the TakagiSugeno (TS) fuzzy approximator. The primary goal is to regulate blood glucose levels by employing robust control strategies for the nonlinear dynamics of the glucose-insulin system, which are described using the Bergman Minimal Model. The proposed approach systematically incorporates insulin pump constraints, such as maximum insulin delivery rates, to ensure practical applicability in real-world scenarios. Simulation results demonstrate that the proposed controller maintains blood glucose levels within a safe range for over 84% of the time, with average glucose levels reduced to as low as 95mg/dL under the least restrictive input constraints. Furthermore, the controller effectively mitigates meal-induced disturbances while minimizing hypoglycemia risks, demonstrating its robustness under varying parameter uncertainties. This research highlights the potential of the proposed method for use in closed-loop insulin delivery systems, offering a promising solution for personalized and adaptive diabetes management.

Highlights

  • Innovative Insulin Dosing: Utilizes Linear Matrix Inequality (LMI) techniques with the Takagi-Sugeno (TS) fuzzy approximator for effective Type 1 Diabetes management.
  • Robust Glucose Regulation: Employs robust control strategies for the nonlinear glucose-insulin dynamics, maintaining safe blood glucose levels over 84% of the time.
  • Practical Application: Incorporates insulin pump constraints, achieving average glucose levels as low as 95 mg/dL and minimizing hypoglycemia risks.
  • Personalized Diabetes Management: Demonstrates potential for closed-loop insulin delivery systems, offering a robust, adaptive solution for diabetes care.

Keywords

LMI
Takagi-Sugeno Fuzzy
Blood Glucose Control
Type 1 Diabetes
Robust Control

Subjects

  1. Atkinson, M. A., Eisenbarth, G. S., & Michels, A. W. (2014). Type 1 diabetes. The lancet, 383(9911), 69-82.
  2. National Institute of Diabetes and Digestive and Kidney Diseases. (n.d.). Type 1 diabetes. National Institutes of Health. Retrieved October 11, 2024, from https://www.niddk.nih.gov/health-information/diabetes/overview/what-is-diabetes/type-1-diabetes
  3. Nathan, D. M. (2005). Long-term complications of diabetes mellitus. New England journal of medicine, 323(25), 2609-2619.
  4. American Diabetes Association. (2021). Complications of diabetes. Retrieved October 11, 2024, from https://www.diabetes.org/diabetes/complications
  5. Cryer, P. E. (1994). Hypoglycemia: the limiting factor in the management of IDDM. Diabetes, 43(11), 1378-1389.
  6. Kovatchev, B., Tamborlane, W. V., Cefalu, W. T., & Cobelli, C. (2016). The artificial pancreas in 2016: a digital treatment ecosystem for diabetes. Diabetes Care, 39(7), 1123.
  7. Steil, G. M., Panteleon, A. E., & Rebrin, K. (2004). Closed-loop insulin delivery—the path to physiological glucose control. Advanced drug delivery reviews, 56(2), 125-144.
  8. Paiva, H. M., Keller, W. S., & da Cunha, L. G. R. (2020). Blood-glucose regulation using fractional-order PID control. Journal of Control, Automation and Electrical Systems, 31(1), 1-9..
  9. Rosales, N., De Battista, H., & Garelli, F. (2022). Hypoglycemia prevention: PID-type controller adaptation for glucose rate limiting in Artificial Pancreas System. Biomedical Signal Processing and Control, 71, 103106.
  10. Hovorka, R., Canonico, V., Chassin, L. J., Haueter, U., Massi-Benedetti, M., Federici, M. O., ... & Wilinska, M. E. (2004). Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiological measurement, 25(4), 905-920.
  11. Kang, S. L., Hwang, Y. N., Kwon, J. Y., & Kim, S. M. (2022). Effectiveness and safety of a model predictive control (MPC) algorithm for an artificial pancreas system in outpatients with type 1 diabetes (T1D): systematic review and meta-analysis. Diabetology & metabolic syndrome, 14(1), 187.
  12. Aiello, E. M., Jaloli, M., & Cescon, M. (2024). Model Predictive Control (MPC) of an artificial pancreas with data-driven learning of multi-step-ahead blood glucose predictors. Control Engineering Practice, 144, 105810.
  13. Lee, H., Buckingham, B. A., Wilson, D. M., & Bequette, B. W. (2009). A closed-loop artificial pancreas using model predictive control and a sliding meal size estimator. diabetes science and technology 3( 5), 1082-1090.
  14. Ebrahimi, N., Ozgoli, S., & Ramezani, A. (2020). Model free sliding mode controller for blood glucose control: Towards artificial pancreas without need to mathematical model of the system. Computer Methods and Programs in Biomedicine, 195, 105663.
  15. El Fathi, A., Ganji, M., Boiroux, D., Bengtsson, H., & Breton, M. D. (2023, August). Intermittent Control for Safe Long-Acting Insulin Intensification for Type 2 Diabetes: In-Silico Experiments. In 2023 IEEE Conference on Control Technology and Applications (CCTA) (pp. 534-539). IEEE.
  16. Nath, A., Dey, R., & Balas, V. E. (2018). Closed loop blood glucose regulation of type 1 diabetic patient using Takagi-Sugeno fuzzy logic control. In Soft Computing Applications: Proceedings of the 7th International Workshop Soft Computing Applications (SOFA 2016), Volume 2 7 (pp. 286-296). Springer International Publishing..
  17. Farahmand, B., Dehghani, M., & Vafamand, N. (2019). Fuzzy model-based controller for blood glucose control in type 1 diabetes: An LMI approach. Biomedical Signal Processing and Control, 54, 101627.
  18. Farahmand, B., Dehghani, M., & Vafamand, N. (2019). Fuzzy model-based controller for blood glucose control in type 1 diabetes: An LMI approach. Biomedical Signal Processing and Control, 54, 101627..
  19. Bergman, R. N. (2006). Minimal model: perspective from 2005. Hormone research, 64(Suppl. 3), 8-15..
  20. Mehran, K. (2008). Takagi-sugeno fuzzy modeling for process control. Industrial Automation, Robotics and Artificial Intelligence (EEE8005), 262, 1-31..
  21. Sala, A., & Arino, C. (2009). Polynomial fuzzy models for nonlinear control: A Taylor series approach. IEEE Transactions on Fuzzy Systems, 17(6), 1284-1295.
  22. Scherer, C., & Weiland, S. (2000). Linear matrix inequalities in control. Lecture Notes, Dutch Institute for Systems and Control, Delft, The Netherlands, 3(2).
  23. Wang, H. S., Yung, C. F., & Chang, F. R. (1998). Bounded real lemma and H∞ control for descriptor systems. IEE Proceedings-Control Theory and Applications, 145(3), 316-322.
  24. Fushimi, E., Rosales, N., De Battista, H., & Garelli, F. (2017, September). Constraints on the insulin infusion for artificial pancreas clinical trials. In 2017 XVII Workshop on Information Processing and Control (RPIC) (pp. 1-6). IEEE.
  25. Khalil, H. K. (2009). Lyapunov stability. Control systems, robotics and automation, 12, 115.
  26. Man, C. D., Micheletto, F., Lv, D., Breton, M., Kovatchev, B., & Cobelli, C. (2014). The UVA/PADOVA type 1 diabetes simulator: new features. Journal of diabetes science and technology, 8(1), 26-34.
  27. GANJIARJENAKI, M., FABRIS, C., EL FATHI, A. N. A. S., LV, D., KOVATCHEV, B., & BRETON, M. D. (2024). 75-OR: In-Silico Replay of Insulin Degludec and Liraglutide Clinical Trial Data in Subjects with Type 2 Diabetes. Diabetes, 73(Supplement_1).
  28. Ganji, M., Fathi, A. E., Fabris, C., Lv, D., Kovatchev, B., & Breton, M. (2024). Distribution-Based Sub-Population Selection (DSPS): A Method for in-Silico Reproduction of Clinical Trials Outcomes. arXiv preprint arXiv:2409.00232.
  29. Mehrnia, M., Kholmovski, E., Katsaggelos, A., Kim, D., Passman, R., & Elbaz, M. S. (2024). Novel Self-Calibrated Threshold-Free Probabilistic Fibrosis Signature Technique for 3D Late Gadolinium Enhancement MRI. IEEE Transactions on Biomedical Engineering.
  30. Hadizadeh Moghaddam, A., Nayebi Kerdabadi, M., Liu, M., & Yao, Z. (2024, October). Contrastive learning on medical intents for sequential prescription recommendation. In Proceedings of the 33rd ACM International Conference on Information and Knowledge Management (pp. 748-757).
  31. Naderi, F., Perez-Raya, I., Yadav, S., Kalajahi, A. P., Mamun, Z. B., & D’Souza, R. M. (2024). Towards chemical source tracking and characterization using physics-informed neural networks. Atmospheric Environment, 334, 120679.
  32. Tezerjani, M. D., Carrillo, D., Qu, D., Dhakal, S., Mirzaeinia, A., & Yang, Q. (2024). Real-time Motion Planning for autonomous vehicles in dynamic environments. arXiv preprint arXiv:2406.02916.
  33. Ferrero, A., Ghelichkhan, E., Manoochehri, H., Ho, M. M., Albertson, D. J., Brintz, B. J., ... & Knudsen, B. S. (2024). HistoEM: A Pathologist-Guided and Explainable Workflow Using Histogram Embedding for Gland Classification. Modern Pathology, 37(4), 100447.
Sustainable Energy and Artificial Intelligence
Volume 1, Issue 2
Spring 2025
Pages 67-75

  • Receive Date 16 September 2024
  • Revise Date 09 December 2024
  • Accept Date 11 December 2024
  • First Publish Date 11 December 2024

Home

Guide for Authors

Submit Manuscript

Reviewers

Contact Us